51,895 research outputs found
Efficient Equilibria in Polymatrix Coordination Games
We consider polymatrix coordination games with individual preferences where
every player corresponds to a node in a graph who plays with each neighbor a
separate bimatrix game with non-negative symmetric payoffs. In this paper, we
study -approximate -equilibria of these games, i.e., outcomes where
no group of at most players can deviate such that each member increases his
payoff by at least a factor . We prove that for these
games have the finite coalitional improvement property (and thus
-approximate -equilibria exist), while for this
property does not hold. Further, we derive an almost tight bound of
on the price of anarchy, where is the number of
players; in particular, it scales from unbounded for pure Nash equilibria ( to for strong equilibria (). We also settle the complexity
of several problems related to the verification and existence of these
equilibria. Finally, we investigate natural means to reduce the inefficiency of
Nash equilibria. Most promisingly, we show that by fixing the strategies of
players the price of anarchy can be reduced to (and this bound is tight)
Smoothed Efficient Algorithms and Reductions for Network Coordination Games
Worst-case hardness results for most equilibrium computation problems have
raised the need for beyond-worst-case analysis. To this end, we study the
smoothed complexity of finding pure Nash equilibria in Network Coordination
Games, a PLS-complete problem in the worst case. This is a potential game where
the sequential-better-response algorithm is known to converge to a pure NE,
albeit in exponential time. First, we prove polynomial (resp. quasi-polynomial)
smoothed complexity when the underlying game graph is a complete (resp.
arbitrary) graph, and every player has constantly many strategies. We note that
the complete graph case is reminiscent of perturbing all parameters, a common
assumption in most known smoothed analysis results.
Second, we define a notion of smoothness-preserving reduction among search
problems, and obtain reductions from -strategy network coordination games to
local-max-cut, and from -strategy games (with arbitrary ) to
local-max-cut up to two flips. The former together with the recent result of
[BCC18] gives an alternate -time smoothed algorithm for the
-strategy case. This notion of reduction allows for the extension of
smoothed efficient algorithms from one problem to another.
For the first set of results, we develop techniques to bound the probability
that an (adversarial) better-response sequence makes slow improvements on the
potential. Our approach combines and generalizes the local-max-cut approaches
of [ER14,ABPW17] to handle the multi-strategy case: it requires a careful
definition of the matrix which captures the increase in potential, a tighter
union bound on adversarial sequences, and balancing it with good enough rank
bounds. We believe that the approach and notions developed herein could be of
interest in addressing the smoothed complexity of other potential and/or
congestion games
Dynamic Coordination via Organizational Routines
We investigate dynamic coordination among members of a problem solving team who receive private signals about which of their actions are required for a (static) coordinated solution and who have repeated opportunities to explore different action combinations. In this environment ordinal equilibria, in which agents condition only on how their signals rank their actions and not on signal strength, lead to simple patterns of behavior that have a natural interpretation as routines. These routine spartially solve the team’s coordination problem by synchronizing the team’s search efforts and prove to be resilient to changes in the environment by being expost equilibria, to agents having only a coarse understanding of other agents’ strategies by being fully cursed, and to natural forms of agents’ overcon?dence. The price of this resilience is that optimal routines are frequently not optimal equilibria
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